This is a substantial update of this reference document. The most important addition is the chain and substitution rules for arithmetic difference calculus (ADC). Other additions include: more properties of the discrete power function, more properties of ADC operators, definitions of analog functions, and ranges of convergence of (some) z-transforms. I also corrected some errors that were discovered since the last version.
Grab it here.
I have updated the Reference for Functional Equations. I have added several entries to the tables, updated the graphs, added some new graphs, added some explanations and additional notes on notation, corrected a few typos, and re-organised the document slightly. Get the new version here.
I decided to put the Poisson disk sampling code here for download since the site that hosted it is down. The code accompanies the tutorial on Dev.Mag: Poisson Disk Sampling.
Tools for editing game levels and AI for your own games are nice to have, but it is not always practical to implement these for small projects, nor is it affordable to buy them off-the-shelf or bundled with expensive middleware.
In the Dev.Mag article Guerrilla Tool Development, I give some ideas for getting some useful tools on a tight budget. Check it out!
I wrote an article for Dev.Mag covering some techniques for working with seamless tile sets such as making blend tiles, getting more variety with procedural colour manipulation, tile placement strategies, and so on.
Check it out!
The Python Image Code has also been updated with some of the algorithms explained in the article.
The example for the tutorial How to Turn XSI Mod Tool into a Level Editor for your XNA Games: Updated for XNA 3.0 have also been updated to work with XNA 3.0. The XSI plug-in has also been tested in the new Mod Tool (7.5).
XSIModToolLevelEditor3.zip (5.2 MB).
In this new version of Reference for Functional Equations I added several more z-transform pairs. I also started to add binomial transform pairs. The definition for the binomial is not consistent among different authors. I arbitrarily chose one, and later I changed it. I will probably change it again. Several typos were fixed. I am working on a system to include proofs so that the tables can be checked more easily.
I have not posted in a while; one reason is that I got sucked into some interesting mathematics; the work-in-progress Reference for Functional Equations is the result. If you are interested in such things – have a look.